Instar Determination of Blattella asahinai (Blattodea: Ectobiidae) From Digital Measurements of the Pronotum Using Gaussian Mixture Modeling and the Number of Cercal Annuli

Abstract

The Asian cockroach, Blattella asahinai Mizukubo, has expanded its range throughout the southeastern United States since its introduction into Florida. Unlike its closest relative, the German cockroach, Blattella germanica (L.), B. asahinai lives outdoors and can fly. There is little information on the biology and development of B. asahinai, including the number of instars during nymphal development. To estimate the number of instars of B. asahinai, nymphs were photographed, sexed, and the lengths and widths of their pronota were measured digitally. The number of instars of B. asahinai was estimated using Gaussian mixture models with the pronotal data. The most probable model and its clusters were selected to assign individuals to an instar. Instars were also determined by counting the number of cercal annuli of nymphs. Both clustering and cercal annuli indicated that B. asahinai most frequently had six instars when reared at 30°C. Growth did not strictly follow the Brooks-Dyar Rule, because nymphs had different numbers of instars and different growth patterns. Although Gaussian mixture models are not efficient for field sampling experiments, digital measurements may provide a way to estimate instars with live specimens in development studies without handling the animals in a way that may alter growth.

Life-History Traits from Embryonic Development to Reproduction in the American Cockroach

“…Such intraspecific variation in nymphal instar numbers is widespread across insect taxa and is found in most major orders, including those of hemimetabolous and holometabolous insects [ 20 ]. For example, in Blattaria, the numbers of nymphal instars in cockroaches, including B. germanica [ 18 , 35 , 36 , 37 , 38 , 39 ], B. asahinai [ 24 ], Diploptera punctata [ 18 , 40 , 41 ] and Periplaneta japonica [ 42 ], are variable. This intraspecific variability in the number of nymphal instars is influenced by factors such as temperature, photoperiod, humidity, nutrition, population density, genetics, and sex [ 20 ].…”

“…Newly hatched first-instar nymphs were collected within 24 h and group-housed. Referring to the modeling method of Blattella asahinai for estimating nymphal instars [ 24 ], the body mass, length, and width of the nymphs were measured as three indicators. Cockroaches were massed on an analytical balance (Sartorius) after anaesthetizing with CO 2 to measure the weight of each cockroach.…”

Instar determination by constrained gaussian mixture models according to Dyar’s rule

“…For cases 5 and 6, groups with an unbalanced mixing proportion, Dyar's rule, and variance homogeneity are assumed. Their mixing proportion imitates a proportion of the first to the sixth instars regarding Blattella asahinai data collected by Peterson et al (2019). Cases 7-12 are variance heterogeneity versions of cases 1-6.…”

“…The log transformation possibly does not guarantee the validity of the normality assumption. Many instar determinations studies assume a normal distribution of observations for each instar stage (Logan et al 1998, Wu et al 2013, Merville et al 2014, whereas the result of Peterson et al (2019) showed that gaussian mixture models using log-transformed data provided more discrete clusters than those using untransformed…”

“…Accordingly, conformity to Dyar’s rule can provide information on growth patterns in an insect species. Many studies about instar determination for an insect species evaluate the conformality of Dyar’s rule to their models (Logan et al 1998, Wu et al 2013, Sukovata 2019, Peterson et al 2019, Nguyen et al 2022). If the result indicates nonconformity to Dyar’s rule, it can be interpreted as underestimating or overestimating the number of instars (Sukovata 2019), or the violation of Dyar’s rule in its growth (Peterson et al 2019).…”